Jungang Wang

Integer ambiguity resolution (IAR) is critical in high‐precision Global Navigation Satellite Systems (GNSS) data processing. While the legacy double‐differenced (DD) IAR is widely adopted by most analysis centers (ACs) of the International GNSS Service, undifferenced (UD) IAR is gaining popularity for global network solutions. Theoretically, DD‐IAR and UD‐IAR should achieve equivalent results. Practically, however, several studies show that the latter preserves better results, which is not clearly explained yet. In this study, we investigate the performance of serval commonly used DD‐IAR and UD‐IAR strategies across key GNSS products, including satellite orbits, station coordinates, earth rotation parameters (ERP), and geocenter coordinates. The results show that UD‐IAR consistently outperforms all conventional DD‐IAR strategies in both orbit and geodetic parameter estimation. Through detailed comparisons, we identify two primary effects that degrade the performance of DD‐IAR: incorrectly fixed ambiguities and insufficient independent fixable ambiguities. Compared to the UD‐IAR solution, about 40% of the differences in satellite orbits from DD‐IAR are linked to incorrectly fixed ambiguities, whereas approximately 45%–71% of the differences in geodetic parameters are associated with insufficient independent fixable ambiguities. When both issues are addressed, DD‐IAR and UD‐IAR yield comparable performance, confirming their theoretical equivalence. However, it is not practical to implement the perfect DD‐IAR free of the two issues mentioned above, particularly in large‐scale networks. In contrast, the UD‐IAR is more robust and efficient, making it is highly suitable for handle thousands of stations. As such, UD IAR is recommended for high‐precision GNSS applications.

Ray-tracing through numerical weather models (NWMs) is one of the most accurate methods for determining slant tropospheric delays (STDs) in microwave remote sensing. However, the massive data volumes of high-resolution NWMs create substantial I/O operations, limiting large-scale ray-tracing on general hardware. This constraint has historically necessitated parameterized tropospheric delay models, which are disseminated as standardized products (e.g., zenith delays with mapping functions and horizontal gradients). Recently, the AI-driven VAE-former algorithm revolutionized NWM compression, achieving >470:1 ratios by compressing 37 pressure level, 0.25°×0.25° ERA5 data into files smaller than surface-only VMF3 products (1°×1° resolution). This breakthrough challenges the conventional reliance on parameterized models as the sole practical solution. We quantified discrepancies in tropospheric delay parameters between original ERA5 and VAEformer-compressed CRA5 data across 2022, evaluating compression fidelity on global grids and against in-situ zenith tropospheric delay (ZTD) estimates. Results show global average precision loss from compression is <2 mm (<5%) for ZTD, with RMSE differences 10 mm). Our findings demonstrate CRA5 as a reliable ERA5 substitute, with compression-induced inaccuracies being negligible for most microwave-based remote sensing applications. This work underscores that parameterized delay modeling is no longer the exclusive pathway, enabling efficient local computation of high-precision STDs without through mapping functions and gradients.

The combination of different space geodetic techniques is essential for providing reliable and precise geodetic reference frames and earth orientation parameters (EOP), where applying ties, that is, constraints on common parameters between different techniques, is critical. A combination at the observation level allows all ties to be properly applied and ensures results with the consistency, precision, and reliability that can hardly be achieved through combination at the parameter or normal equation level. In this study, we realize integrated GPS and VLBI processing at the observation level during five VLBI CONT campaigns (CONT05 to CONT17). We investigate the impact of applying different types of ties in the integrated solution on both station coordinates and the EOP, including global ties (i.e., EOP), station coordinate ties, and tropospheric ties. We demonstrate that the large number of GPS observations plays a dominant role in the integrated solution and yields more precise estimates of polar motion and station coordinate, while the comparatively smaller number of VLBI observations provides the full set of EOP, especially UT1-UTC and CPO. The VLBI network becomes more stable when the ties are applied, with station coordinate repeatability improved by up to 20% horizontally and 30% vertically. Compared to the IERS EOP 14 C04 product, the EOP precisions of the integrated solution are approximately 40 μas for polar motion, 10 μs for UT1-UTC, and about 45 μas for celestial pole offsets (CPO). The integrated processing improves the agreement of CPO components with respect to IERS EOP 14 C04 by up to 10%. Inspecting day-boundary discontinuities, the integrated processing improves the y-pole component by 10% to 15% and UT1-UTC by around 20%. This study constitutes a solid basis for the consistent realization of reference frames and EOP at the observation level.

High-quality precipitable water vapor (PWV) plays a vital role in climate change and weather prediction studies. This research introduces a novel scheme for retrieving high-resolution surface-domain PWV with real-time and forecasting capabilities with global coverage, utilizing weather forecast foundation models represented by Huawei Cloud Pangu-Weather, Google DeepMind GraphCast, and Shanghai AI Lab FengWu. The accuracy of the new scheme is cross-validated against PWVs from radiosondes, Global Navigation Satellite Systems (GNSSs), and the fifth generation ECMWF reanalysis (ERA5). Results show the new scheme achieves 3.01 mm global root mean square error (RMSE) in real-time, and the value reduce to 2.25 mm when focusing only on land areas, which is more accurate than most existing methods that rely on post-processed surface-domain data. The poor accuracy in low-latitude and mid-latitude ocean regions limits the accuracy of the new scheme and future integration of GNSS PWV data from ocean sources is expected to improve it. Overall, the proposed scheme demonstrates very satisfactory global PWV accuracy and has the potential for further improvement with the development of artificial intelligence.

Non‐tidal loading (NTL) introduces surface deformation on the Earth and increases the variability in coordinates measured by space geodetic techniques. Correcting NTL displacements in Global Navigation Satellite Systems (GNSS) analysis has been discussed extensively, commonly at the parameter level. We investigate the three levels of correcting non‐tidal atmospheric and oceanic loading (NTAOL) displacements systematically in long‐term analysis of GNSS global network solution, including the observation, normal equation, and parameter levels. The difference between the observation and normal equation levels lies in addressing high‐frequency (sub‐daily) displacements, and that between the normal equation and parameter levels concerns datum realization. Correcting NTAOL at the observation (or normal equation) level improves the station coordinate repeatability by 3%–4% horizontally and 13% vertically, slightly greater than that at the parameter level by 0.5%. Discrepancies in station coordinates between the observation (or normal equation) and the parameter level are minor but systematic, and the horizontal discrepancies can be largely reduced by Helmert transformation. These transformation parameters correspond to the datum parameters, including polar motion offsets and geocenter coordinates. High‐frequency loading displacements mainly impact site‐wise tropospheric parameters and especially receiver clocks, albeit with small magnitudes at the sub‐mm level. Satellite orbits in the along and cross components are affected by both datum differences (between normal equation and parameter levels) and high‐frequency displacements (between observation and normal equation levels), while radial component and satellite clocks are solely affected by the latter.

The global high-precision Terrestrial Reference Frame (TRF) is determined through the combination of the four space geodetic techniques: VLBI, SLR, GNSS, and DORIS. The multi-technique combination heavily relies on the common objects or parameters, i.e., the ties, which link the different techniques. Current realizations of the International Terrestrial Reference Frame (ITRF) employ local ties and Earth Orientation Parameter (EOP). Additional ties such as tropospheric ties and satellite orbit ties are being explored. Another promising approach is using clock ties, where co-located instruments connected to a common clock enable intra- and inter-technique clock tie modeling.Clock ties between GNSS and VLBI are of particular interest as (1) GNSS provides dense observations at every epoch, allowing the epoch-wise estimation of clock parameters, and (2) VLBI typically relies on clock modeling due to the insufficient number of observations per epoch. Using the GNSS and VLBI co-location stations during VLBI CONT campaigns, we demonstrate inter-technique clock agreements within 0.1 and 0.2 ns for short (24-hour) and long (15-day) periods, respectively. We further explore the application of clock ties in the GNSS and VLBI integrated solution, focusing on the impact on station coordinates and tropospheric delays. We also address the challenges of modeling deterministic and stochastic components of the clock ties, highlighting their potential to improve the precision of TRF realizations.

Accurate modeling of tropospheric delay is important for high-precision data analysis of space geodetic techniques, such as the Global Navigation Satellite System (GNSS). Empirical tropospheric delay models provide zenith delays with an accuracy of 3 to 4 cm globally and do not rely on external meteorological input. They are thus important for providing a priori delays and serving as constraint information to improve the convergence of real-time GNSS positioning, and in the latter case proper weighting is critical. Currently, empirical tropospheric delay models only provide delay values but not the uncertainty of delays. For the first time, we present a global empirical tropospheric delay model, which provides both the zenith delay and the corresponding uncertainty, based on 10 years of tropospheric delays from numerical weather models (NWMs). The model is based on a global grid and, at each grid point, a set of parameters that describes the delay and uncertainty in the constant, annual, and semiannual terms. The empirically modeled zenith delay has agreements of 36 and 38 mm compared to 3-year delay values from the NWM and 4-year estimates from GNSS stations, which is comparable to previous models such as Global Pressure and Temperature 3 (GPT3). The modeled zenith tropospheric delay (ZTD) uncertainty shows a correlation of 96 % with the accuracy of the empirical ZTD model over 380 GNSS stations over the 4 years. For GNSS stations where the uncertainty annual amplitude is larger than 20 mm, the temporal correlation between the formal error and smoothed accuracy reaches 85 %. Using GPS observations from ∼ 200 globally distributed IGS stations processed in kinematic precise point positioning (PPP) mode over 4 months in 2020, we demonstrate that using proper constraints can improve the convergence speed. The formal error modeling is based on a similar dataset to that of the GPT series, and thus it is also applicable for these empirical models.

Kinematic airborne platforms are becoming increasingly vital for Earth observation. They highlight the critical need for accurate tropospheric delay corrections across varying altitudes, especially as most existing models are limited to Earth's surface. Although analytical functions have been used to model vertical reductions in tropospheric delays, they struggle to capture the intricate vertical variations of atmospheric state. In response, we introduce a novel approach that utilizes deep neural networks (DNN) to reconstruct global three‐dimensional zenith hydrostatic delay (ZHD) and zenith wet delays (ZWD) derived from numerical weather models (NWM). Our method reconstructs NWM‐derived ZHD and ZWD globally up to 14 km above the Earth's surface, with average precision levels of 0.4 and 0.8 mm, respectively. Compared to the analytical third‐order exponential model, the DNN approach demonstrates substantial improvement with global average root‐mean‐square reductions of 63% for ZHD and 36% for ZWD.